Quantum energy gap law of outer-sphere electron transfer reactions: A molecular dynamics study on aqueous solution

Journal of Chemical Physics

Volumn 106, Issue 1, 1997, Pages 116-126

  Ando, Koji ^a,b  

^a INST OF PHYS AND CHEMICAL RESEARCH   (Japan)

^b UNIVERSITY OF TSUKUBA   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ACTIVATION ENERGY; COMPUTER SIMULATION; CORRELATION METHODS; ENERGY GAP; EQUATIONS OF MOTION; ISOTOPES; MOLECULAR DYNAMICS; QUANTUM THEORY; RELAXATION PROCESSES; WATER;

DONOR ACCEPTOR DISTANCE; ELECTRON TRANSFER; QUANTUM ENERGY GAP LAW; QUANTUM RATE CONSTANTS; SOLVENT REORGANIZATION ENERGIES; SPECTRAL DENSITY; TIME CORRELATION FUNCTIONS;

CHARGE TRANSFER;

EID: 0030822969     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.473037     Document Type: Article

References (91)

1. H. Beens and A. Weller, in Organic Molecular Photophysics, edited by J. B. Birks (Wiley Interscience, London, 1975); Dynamics and Mechanisms of Photoinduced Electron Transfer and Related Phenomena, edited by N. Mataga, T. Okada, and H. Masuhara (Elsevier, Amsterdam, 1992); Electron and Proton Transfer Processes in Chemistry and Biology, edited by A. Müller, H. Ratajczak, W. Junge, and E. Diemann (Elsevier, Amsterdam, 1992).
2. H. Beens and A. Weller, in Organic Molecular Photophysics, edited by J. B. Birks (Wiley Interscience, London, 1975); Dynamics and Mechanisms of Photoinduced Electron Transfer and Related Phenomena, edited by N. Mataga, T. Okada, and H. Masuhara (Elsevier, Amsterdam, 1992); Electron and Proton Transfer Processes in Chemistry and Biology, edited by A. Müller, H. Ratajczak, W. Junge, and E. Diemann (Elsevier, Amsterdam, 1992).
3. H. Beens and A. Weller, in Organic Molecular Photophysics, edited by J. B. Birks (Wiley Interscience, London, 1975); Dynamics and Mechanisms of Photoinduced Electron Transfer and Related Phenomena, edited by N. Mataga, T. Okada, and H. Masuhara (Elsevier, Amsterdam, 1992); Electron and Proton Transfer Processes in Chemistry and Biology, edited by A. Müller, H. Ratajczak, W. Junge, and E. Diemann (Elsevier, Amsterdam, 1992).
4. J. Ulstrup, Charge Transfer Processes in Condensed Media (Springer, Berlin, 1979).
5. M. D. Newton and N. Sutin, Annu. Rev. Phys. Chem. 35, 437 (1984); R. A. Marcus and N. Sutin, Biochim. Biophys. Acta. 811, 265 (1985).
6. M. D. Newton and N. Sutin, Annu. Rev. Phys. Chem. 35, 437 (1984); R. A. Marcus and N. Sutin, Biochim. Biophys. Acta. 811, 265 (1985).
7. R. A. Marcus, J. Chem. Phys. 24, 966, 979 (1956); Ann. Rev. Phys. Chem. 15, 155 (1964).
8. R. A. Marcus, J. Chem. Phys. 24, 966, 979 (1956); Ann. Rev. Phys. Chem. 15, 155 (1964).
9. For example, A. J. Leggett, S. Chakravarty, A. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, Rev. Mod. Phys. 59, 1 (1987) and references therein.
10. J. K. Hwang and A. Warshel, J. Am. Chem. Soc. 109, 715 (1987); A. Warshel and J. K. Hwang, J. Chem. Phys. 84, 4938 (1986); A. Warshel, Z. T. Chu, and W. W. Parson, Science 246, 112 (1989).
11. J. K. Hwang and A. Warshel, J. Am. Chem. Soc. 109, 715 (1987); A. Warshel and J. K. Hwang, J. Chem. Phys. 84, 4938 (1986); A. Warshel, Z. T. Chu, and W. W. Parson, Science 246, 112 (1989).
12. J. K. Hwang and A. Warshel, J. Am. Chem. Soc. 109, 715 (1987); A. Warshel and J. K. Hwang, J. Chem. Phys. 84, 4938 (1986); A. Warshel, Z. T. Chu, and W. W. Parson, Science 246, 112 (1989).
13. J. S. Bader, R. A. Kuharski, and D. Chandler, J. Chem. Phys. 93, 230 (1990).
14. C. L. Kneifel, M. D. Newton, and H. L. Friedman, J. Mol. Liq. 60, 107 (1994).
15. D. Rehm and A. Weller, Isr. J. Chem. 8, 259 (1970); A. Kira, J. Phys. Chem. 85, 3047 (1981); G. L. Closs, L. T. Calcaterra, N. J. Green, K. W. Penfield, and J. R. Miller, ibid. 90, 3673 (1986).
16. D. Rehm and A. Weller, Isr. J. Chem. 8, 259 (1970); A. Kira, J. Phys. Chem. 85, 3047 (1981); G. L. Closs, L. T. Calcaterra, N. J. Green, K. W. Penfield, and J. R. Miller, ibid. 90, 3673 (1986).
17. D. Rehm and A. Weller, Isr. J. Chem. 8, 259 (1970); A. Kira, J. Phys. Chem. 85, 3047 (1981); G. L. Closs, L. T. Calcaterra, N. J. Green, K. W. Penfield, and J. R. Miller, ibid. 90, 3673 (1986).
18. M. Tachiya, J. Phys. Chem. 93, 7050 (1989); A. Yoshimori, T. Kakitani, Y. Enomoto, N. Mataga, ibid. 93, 8316 (1989); J. Tang, J. Chem. Phys. 99, 5828 (1993).
19. M. Tachiya, J. Phys. Chem. 93, 7050 (1989); A. Yoshimori, T. Kakitani, Y. Enomoto, N. Mataga, ibid. 93, 8316 (1989); J. Tang, J. Chem. Phys. 99, 5828 (1993).
20. M. Tachiya, J. Phys. Chem. 93, 7050 (1989); A. Yoshimori, T. Kakitani, Y. Enomoto, N. Mataga, ibid. 93, 8316 (1989); J. Tang, J. Chem. Phys. 99, 5828 (1993).
21. P. Siders and R. A. Marcus, J. Am. Chem. Soc. 103, 741, 748 (1981).
22. R. A. Marcus and P. Siders, J. Phys. Chem. 86, 622 (1982).
23. It is noted that the high-temperature formula for harmonic systems does not include entropy terms coming from frequency changes. Equation (1.1) is more general in this respect.
24. R. Kubo and Y. Toyozawa, Prog. Theor. Phys. 13, 160 (1955).
25. M. Lax, J. Chem. Phys. 20, 1752 (1952).
26. J. J. Hopfield, Proc. Natl. Acad. Sci. USA 71, 3640 (1974).
27. P. G. Wolynes, J. Chem. Phys. 87, 6559 (1987).
28. C. Zheng, J. A. McCammon, and P. G. Wolynes, Proc. Natl. Acad. Sci. USA 86, 6441 (1989); C. H. Mak and J. N. Gehlen, Chem. Phys. Lett. 206, 130 (1993); R. Egger and C. H. Mak, J. Chem. Phys. 99, 2541 (1993).
29. C. Zheng, J. A. McCammon, and P. G. Wolynes, Proc. Natl. Acad. Sci. USA 86, 6441 (1989); C. H. Mak and J. N. Gehlen, Chem. Phys. Lett. 206, 130 (1993); R. Egger and C. H. Mak, J. Chem. Phys. 99, 2541 (1993).
30. C. Zheng, J. A. McCammon, and P. G. Wolynes, Proc. Natl. Acad. Sci. USA 86, 6441 (1989); C. H. Mak and J. N. Gehlen, Chem. Phys. Lett. 206, 130 (1993); R. Egger and C. H. Mak, J. Chem. Phys. 99, 2541 (1993).
31. M. Maroncelli and G. R. Fleming, J. Chem. Phys. 89, 5044 (1988).
32. K. Ando and S. Kato, J. Chem. Phys. 95, 5966 (1991).
33. M. Cho, G. R. Fleming, S. Saito, I. Ohmine, and R. M. Stratt, J. Chem. Phys. 100, 6672 (1994).
34. K. Ando, J. Chem. Phys. 101, 2850 (1994).
35. M. D. Newton, Int. J. Quantum Chem. S 14, 363 (1980); Y.-P. Liu and M. D. Newton, J. Phys. Chem. 99, 12382 (1995); G. Karlström P.-A. Malmqvist J. Chem. Phys. 96, 6115 (1992).
36. M. D. Newton, Int. J. Quantum Chem. S 14, 363 (1980); Y.-P. Liu and M. D. Newton, J. Phys. Chem. 99, 12382 (1995); G. Karlström P.-A. Malmqvist J. Chem. Phys. 96, 6115 (1992).
37. M. D. Newton, Int. J. Quantum Chem. S 14, 363 (1980); Y.-P. Liu and M. D. Newton, J. Phys. Chem. 99, 12382 (1995); G. Karlström P.-A. Malmqvist J. Chem. Phys. 96, 6115 (1992).
38. For example, M. P. Allen and D. J. Tidesley, Computer Simulation of Liquids (Clarendon, Oxford, 1987).
39. W. L. Jorgensen, J. Chandrasekhar, J. Madura, R. W. Impey, and M. L. Klein, J. Chem. Phys. 79, 926 (1983).
40. L. X. Dang and B. M. Pettitt, J. Phys. Chem. 91, 3349 (1987).
41. C. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations (Prentice-Hall, Englewood Cliffs, 1971).
42. For example, W. L. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, New York, 1989).
43. W. F. van Gunsteren and H. J. C. Berendsen, Mol. Phys. 34, 1311 (1977).
44. micro=0.1 fs. The r-RESPA method was used only for the cooling and equilibration runs and not for the production runs reported in text.
45. H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. Di Nola, and J. R. Haak, J. Chem. Phys. 81, 3684 (1984).
46. M. Tuckerman, B. J. Berne, and G. J. Martyna, J. Chem. Phys. 97, 1990 (1992).
47. The usefulness of the ΔV coordinate is also seen in its connection to the Franck-Condon surface hopping picture, as the two diabatic potentials always coincide at ΔV=0. See also the golden-rule rate formula of Eq. (3.17).
48. The simulation uncertainties were evaluated with the use of the correlation time computed from the TCF of Sec. III B. See Chapter 6 of Ref. 24.
49. M. Tachiya and S. Murata, J. Phys. Chem. 96, 8441 (1992); M. Tachiya and M. Hilczer, in Ultrafast Reaction Dynamics and Solvent Effects: Theoretical and Experimental Aspects, edited by Y. Gauduel and P. J. Rossky (AIP, New York, 1994).
50. M. Tachiya and S. Murata, J. Phys. Chem. 96, 8441 (1992); M. Tachiya and M. Hilczer, in Ultrafast Reaction Dynamics and Solvent Effects: Theoretical and Experimental Aspects, edited by Y. Gauduel and P. J. Rossky (AIP, New York, 1994).
51. It is possible to generalize Eq. (3.3) to take account of the cavity overlap: B. J. Gertner, K. Ando, R. Bianco, J. T. Hynes, Chem. Phys. 183, 309 (1994).
52. For discussions on different polar solvents (acetonitrile and methyl chloride), M. Maroncelli, J. Chem. Phys. 94, 2034 (1991); E. A. Carter and J. T. Hynes, ibid. 94, 5961 (1991).
53. For discussions on different polar solvents (acetonitrile and methyl chloride), M. Maroncelli, J. Chem. Phys. 94, 2034 (1991); E. A. Carter and J. T. Hynes, ibid. 94, 5961 (1991).
54. -1.
55. Our J(ω)/ω corresponds (apart from a constant factor) to I (ω) in Ref. 8 for ferros-ferric exchange ET in a flexible water model. They also computed the spectra of the hydrogen atom velocity-auto-correlation functions, which shows a broad stretching band coming from the strong coordination of the ligand water to the small ions. Its peak position notably shifts depending on the ion charge.
56. L. D. Zusman, Chem. Phys. 49, 295 (1980); ibid. 80, 29 (1983); H. Sumi and R. A. Marcus, J. Chem. Phys. 84, 4894 (1985); A. Garg, J. N. Onuchic, and V. Ambegaokar, ibid. 83, 4491 (1985); J. Jortner and M. Bixon, ibid. 88, 167 (1988); T. Fonseca, ibid. 91, 2869 (1989).
57. L. D. Zusman, Chem. Phys. 49, 295 (1980); ibid. 80, 29 (1983); H. Sumi and R. A. Marcus, J. Chem. Phys. 84, 4894 (1985); A. Garg, J. N. Onuchic, and V. Ambegaokar, ibid. 83, 4491 (1985); J. Jortner and M. Bixon, ibid. 88, 167 (1988); T. Fonseca, ibid. 91, 2869 (1989).
58. L. D. Zusman, Chem. Phys. 49, 295 (1980); ibid. 80, 29 (1983); H. Sumi and R. A. Marcus, J. Chem. Phys. 84, 4894 (1985); A. Garg, J. N. Onuchic, and V. Ambegaokar, ibid. 83, 4491 (1985); J. Jortner and M. Bixon, ibid. 88, 167 (1988); T. Fonseca, ibid. 91, 2869 (1989).
59. L. D. Zusman, Chem. Phys. 49, 295 (1980); ibid. 80, 29 (1983); H. Sumi and R. A. Marcus, J. Chem. Phys. 84, 4894 (1985); A. Garg, J. N. Onuchic, and V. Ambegaokar, ibid. 83, 4491 (1985); J. Jortner and M. Bixon, ibid. 88, 167 (1988); T. Fonseca, ibid. 91, 2869 (1989).
60. L. D. Zusman, Chem. Phys. 49, 295 (1980); ibid. 80, 29 (1983); H. Sumi and R. A. Marcus, J. Chem. Phys. 84, 4894 (1985); A. Garg, J. N. Onuchic, and V. Ambegaokar, ibid. 83, 4491 (1985); J. Jortner and M. Bixon, ibid. 88, 167 (1988); T. Fonseca, ibid. 91, 2869 (1989).
61. L. D. Zusman, Chem. Phys. 49, 295 (1980); ibid. 80, 29 (1983); H. Sumi and R. A. Marcus, J. Chem. Phys. 84, 4894 (1985); A. Garg, J. N. Onuchic, and V. Ambegaokar, ibid. 83, 4491 (1985); J. Jortner and M. Bixon, ibid. 88, 167 (1988); T. Fonseca, ibid. 91, 2869 (1989).
62. B. B. Smith, A. Staib, and J. T. Hynes, Chem. Phys. 176, 521 (1993).
63. G. C. Walker, E. Åkesson, A. E. Johnson, N. E. Levinger, and P. F. Barbara, J. Phys. Chem. 96, 3728 (1992); K. Tominaga, D. A. V. Kliner, A. E. Johnson, N. E. Levinger, and P. F. Barbara, J. Chem. Phys. 98, 1228 (1993).
64. G. C. Walker, E. Åkesson, A. E. Johnson, N. E. Levinger, and P. F. Barbara, J. Phys. Chem. 96, 3728 (1992); K. Tominaga, D. A. V. Kliner, A. E. Johnson, N. E. Levinger, and P. F. Barbara, J. Chem. Phys. 98, 1228 (1993).
65. 0 may become important, which could be adequately modeled by employing averaged force constants.
66. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
67. D. Chandler and P. G. Wolynes, J. Chem. Phys. 74, 4078 (1981).
68. In other words, Λ is related to a "quantum-corrected variance of distribution" of the solvent coordinate (Ref. 16).
69. J. S. Bader and B. J. Berne, J. Chem. Phys. 100, 8359 (1994).
70. H. Sumi, J. Phys. Soc. Jpn. 49, 1701 (1980); M. Sparpaglione and S. Mukamel, J. Chem. Phys. 88, 3263 (1988).
71. H. Sumi, J. Phys. Soc. Jpn. 49, 1701 (1980); M. Sparpaglione and S. Mukamel, J. Chem. Phys. 88, 3263 (1988).
72. N. Shima and M. Tsukada, Surf. Sci. 194, 3121 (1988); M. Tsukada and Z. W. Gortel, Phys. Rev. B 38, 3892 (1988).
73. N. Shima and M. Tsukada, Surf. Sci. 194, 3121 (1988); M. Tsukada and Z. W. Gortel, Phys. Rev. B 38, 3892 (1988).
74. J. N. Onuchic and P. G. Wolynes, J. Phys. Chem. 92, 6495 (1988); J. M. Jean, R. A. Friesner, and G. R. Fleming, J. Chem. Phys. 96, 5827 (1992); R. D. Coalson, D. G. Evans, and A. Nitzan, ibid. 101, 436 (1994).
75. J. N. Onuchic and P. G. Wolynes, J. Phys. Chem. 92, 6495 (1988); J. M. Jean, R. A. Friesner, and G. R. Fleming, J. Chem. Phys. 96, 5827 (1992); R. D. Coalson, D. G. Evans, and A. Nitzan, ibid. 101, 436 (1994).
76. J. N. Onuchic and P. G. Wolynes, J. Phys. Chem. 92, 6495 (1988); J. M. Jean, R. A. Friesner, and G. R. Fleming, J. Chem. Phys. 96, 5827 (1992); R. D. Coalson, D. G. Evans, and A. Nitzan, ibid. 101, 436 (1994).
77. For recent works, see, for example, P. J. Rossky and J. D. Simon, Nature (London) 370, 263 (1994); E. Neria and A. Nitzan, J. Chem. Phys. 99, 1109 (1993); Y. Kimura, J. C. Alfano, P. K. Walhout, and P. F. Barbara, J. Phys. Chem. 98, 3450 (1994).
78. For recent works, see, for example, P. J. Rossky and J. D. Simon, Nature (London) 370, 263 (1994); E. Neria and A. Nitzan, J. Chem. Phys. 99, 1109 (1993); Y. Kimura, J. C. Alfano, P. K. Walhout, and P. F. Barbara, J. Phys. Chem. 98, 3450 (1994).
79. For recent works, see, for example, P. J. Rossky and J. D. Simon, Nature (London) 370, 263 (1994); E. Neria and A. Nitzan, J. Chem. Phys. 99, 1109 (1993); Y. Kimura, J. C. Alfano, P. K. Walhout, and P. F. Barbara, J. Phys. Chem. 98, 3450 (1994).
80. For example, G. W. Robinson, P. J. Thistlethwaite, and J. Lee, J. Phys. Chem. 90, 4224 (1986); A. S. Davydov, Solitons in Molecular Systems (Naukovaja Dumka, Kiev, 1984); T. Komatsuzaki and I. Ohmine, Chem. Phys. 180, 239 (1994); Mol. Sim. 16, 321 (1996); M. Tuckerman, K. Laasonen, M. Sprik, and M. Parrinello, J. Phys. Chem. 99, 5749 (1995); J. Chem. Phys. 103, 150 (1995).
81. For example, G. W. Robinson, P. J. Thistlethwaite, and J. Lee, J. Phys. Chem. 90, 4224 (1986); A. S. Davydov, Solitons in Molecular Systems (Naukovaja Dumka, Kiev, 1984); T. Komatsuzaki and I. Ohmine, Chem. Phys. 180, 239 (1994); Mol. Sim. 16, 321 (1996); M. Tuckerman, K. Laasonen, M. Sprik, and M. Parrinello, J. Phys. Chem. 99, 5749 (1995); J. Chem. Phys. 103, 150 (1995).
82. For example, G. W. Robinson, P. J. Thistlethwaite, and J. Lee, J. Phys. Chem. 90, 4224 (1986); A. S. Davydov, Solitons in Molecular Systems (Naukovaja Dumka, Kiev, 1984); T. Komatsuzaki and I. Ohmine, Chem. Phys. 180, 239 (1994); Mol. Sim. 16, 321 (1996); M. Tuckerman, K. Laasonen, M. Sprik, and M. Parrinello, J. Phys. Chem. 99, 5749 (1995); J. Chem. Phys. 103, 150 (1995).
83. For example, G. W. Robinson, P. J. Thistlethwaite, and J. Lee, J. Phys. Chem. 90, 4224 (1986); A. S. Davydov, Solitons in Molecular Systems (Naukovaja Dumka, Kiev, 1984); T. Komatsuzaki and I. Ohmine, Chem. Phys. 180, 239 (1994); Mol. Sim. 16, 321 (1996); M. Tuckerman, K. Laasonen, M. Sprik, and M. Parrinello, J. Phys. Chem. 99, 5749 (1995); J. Chem. Phys. 103, 150 (1995).
84. For example, G. W. Robinson, P. J. Thistlethwaite, and J. Lee, J. Phys. Chem. 90, 4224 (1986); A. S. Davydov, Solitons in Molecular Systems (Naukovaja Dumka, Kiev, 1984); T. Komatsuzaki and I. Ohmine, Chem. Phys. 180, 239 (1994); Mol. Sim. 16, 321 (1996); M. Tuckerman, K. Laasonen, M. Sprik, and M. Parrinello, J. Phys. Chem. 99, 5749 (1995); J. Chem. Phys. 103, 150 (1995).
85. For example, G. W. Robinson, P. J. Thistlethwaite, and J. Lee, J. Phys. Chem. 90, 4224 (1986); A. S. Davydov, Solitons in Molecular Systems (Naukovaja Dumka, Kiev, 1984); T. Komatsuzaki and I. Ohmine, Chem. Phys. 180, 239 (1994); Mol. Sim. 16, 321 (1996); M. Tuckerman, K. Laasonen, M. Sprik, and M. Parrinello, J. Phys. Chem. 99, 5749 (1995); J. Chem. Phys. 103, 150 (1995).
86. K. Ando and J. T. Hynes, J. Mol. Liq. 64, 25 (1995); Discuss. Faraday Soc. (in press).
87. K. Ando and J. T. Hynes, J. Mol. Liq. 64, 25 (1995); Discuss. Faraday Soc. (in press).
88. For example, W. P. Jencks, Catalysis in Chemistry and Enzymology (McGraw-Hill, New York, 1969); M. Eigen, W. Kruse, and L. De Maeyer, Prog. React. Kin. 2, 285 (1964); W. J. Albery, ibid. 4, 353 (1967); K. Laasonen and M. L. Klein, J. Am. Chem. Soc. 116, 11620 (1994).
89. For example, W. P. Jencks, Catalysis in Chemistry and Enzymology (McGraw-Hill, New York, 1969); M. Eigen, W. Kruse, and L. De Maeyer, Prog. React. Kin. 2, 285 (1964); W. J. Albery, ibid. 4, 353 (1967); K. Laasonen and M. L. Klein, J. Am. Chem. Soc. 116, 11620 (1994).
90. For example, W. P. Jencks, Catalysis in Chemistry and Enzymology (McGraw-Hill, New York, 1969); M. Eigen, W. Kruse, and L. De Maeyer, Prog. React. Kin. 2, 285 (1964); W. J. Albery, ibid. 4, 353 (1967); K. Laasonen and M. L. Klein, J. Am. Chem. Soc. 116, 11620 (1994).
91. For example, W. P. Jencks, Catalysis in Chemistry and Enzymology (McGraw-Hill, New York, 1969); M. Eigen, W. Kruse, and L. De Maeyer, Prog. React. Kin. 2, 285 (1964); W. J. Albery, ibid. 4, 353 (1967); K. Laasonen and M. L. Klein, J. Am. Chem. Soc. 116, 11620 (1994).